[bvan]

Nicely done. I have the same challenge with Bayesian stats and usually do not understand why there is such controversy. It isn’t a question of either/or, except in the minds of academics who rarely venture out into the real world, or have to balance intellectual purity with getting a job done.

In the very first example, a practitioner would consciously have to decide (i.e. make the assumption) whether the number of side on the die (n) is known and deterministic. Once that decision is made, the framework with which observations are evaluated and statistical reasoning applied will forever be conditional on that assumption.. unless it is revised. Practitioners are generally OK with that, whether it leads to ‘Bayesian’ or ‘frequentist’ analysis, and move on.